5. Please help and snow work

The numbers are -3 and 6

From the information given, let the number be x;

the expression is given as;

(√3x + 2) = x - 4

To determine the number, find the square of both sides, we have;

(√3x + 2) ^2 = (x - 4)^2

Find the square of both sides

3x + 2 = ( x - 4)(x + 4); difference of two squares

expand the bracket

3x + 2 = x^2 + 4x - 4x - 16

collect like terms

x^2 - 3x - 16 - 2

x^2 - 3x - 18

x^2 - 6x + 3x - 18

Factorize the expression

x( x - 6) + 3( x - 6)

(x + 3) or (x - 6)

x = -3 or x = 6

Thus, the numbers are -3 and 6

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The given function is greater than or equal to 0 for the interval given as follows:

{x | x ≤ -3 or -1 ≤ x ≤ 0 or x ≥ 2}.

For this problem, with a closed interval, we have that the function is above for:

x ≤ -3, -1 ≤ x ≤ 0, x ≥ 2.

Hence the interval notation is:

{x | x ≤ -3 or -1 ≤ x ≤ 0 or x ≥ 2}.

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Answer: 7

Step-by-step explanation: A polygon has vertices whose coordinates are A(1, 4), B(4, -1), C(-1, -4), and D(-4, 1). Use the midpoint formula to determine whether or not the diagonals

Answer:

7

Step-by-step explanation:

:D

Answer:

Step-by-step explanation:

Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {}, for example, A = {1,2,3,4}

Finite And Infinite Sets: Union Of Sets

Power Set: Complement Of A Set

Equivalent Sets: Universal Set

Types Of Sets: Set Theory

Answer:

70 in^2

Step-by-step explanation:

Make a line through the middle separating the 5 by 5 square and the rectangle. Then you find the individual areas of each. The bottom shape is a 5 by 5 square, so 5*5 is 25. The top shape's length is 5+2+2 because the bottom shape is a square, so each side=5. Then the blank space between both of the length 2's is 5. As a result, the rectangle's dimensions is 9 by 5. 9*5=45. When we add both areas, we get 45+25=70

the answer to your question is Ettwice is 45 years old and Mavis is 15 years old. hope this helps

Step-by-step explanation:

15 * 3 = 45

45 + 15 = 60

Answer:

A. tenths

because there's only two digits after a comma

The hotel charge in city one is $767 and the hotel charge in city two is $2276.

Let x = the charge in 1st city before taxes and

Let y = the charge in 2nd city before taxes

The equation before taxes:

y = x ₊ 1500 ..eq(1)

The equation for total tax paid:

0.075x ₊ 0.055y = 700 ..eq(2)

Substitute equation 1 that is y value in equation 2.

0.075x ₊ 0.055(x₊1500) = 700

0.075x ₊ 0.055x ₊ 82.5 = 700

add the variables and subtract the constants.

0.805x = 700 ₋ 82.5

0.805x = 617.5

x = 617.5/0.805

x = 767

now substitute x value in equation 1.

y = 767 ₊ 1500

y = 2267

Hence the hotel charge before the tax in the first city was $767 and in the second city was $2267.

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Using proportions, the financial measures for the home purchase are given as follows:

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using the unit rates, which along with operations such as multiplication or division are used to find the equivalent measures.

For this problem, the beginning balance is the purchase value of the home, hence:

Beginning Balance: $220,000.

15% of that goes towards the down payment, hence:

0.15 x 220,000 = $33,000.

Payment toward principal: $33,000.

The number of monthly payments is given by:

20 x 12 = 360 monthly payments.

Considering the monthly payment, the ending balance is given as follows:

33,000 + 360 x 1,152.99 = $448,076.4.

Hence the interest owed is:

448,076.4 - 220,000 = $228,076.4.

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Answer:

Step-by-step explanation:

8.2% of what amount is $2.87

2.87 : 8.2 * 100 =

35

The amount due at maturity on Andres Michael's loan of interest rate of 3.75% is $20,431.75

What is effective monthly loan interest rate?

The loan effective monthly interest rate can be determined as the annual interest rate of 3.75% divided by 12 since there are 12 months in a year

effective monthly interest rate=3.75%/12

effective monthly interest rate=0.003125

loan balance after 4 months=$24,440*(1+0.003125)^4- $4,410

loan balance after 4 months=$20,336.94

loan balance after 12 months=$20,336.94*(1+0.003125)^8-$2,590

loan balance after 12 months=$18,260.96

balance at the 4 year(after another 36 months)=$18,260.96*(1+0.003125)^36

balance at the 4 year(after another 36 months)=$20,431.75

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The rate of margin used is 37.5% . The cost price of the batch of plywood is $312.5. Fence post sell for $16. The selling price was $133.33

Margin is the difference between the Selling price and the cost price. The price at which a item is sold is called the selling price and the price at which an item is bought is called the cost price.

The given markup is 60%.

We know that margin=markup÷(1+markup)

markup=60%

Substituting the values we get the rate of margin:

[tex]=\frac{\frac{60}{100} }{1+\frac{60}{100} } \\=\frac{60}{160}\\ =37.5[/tex]

Hence the rate of margin is 37.5 %.

Selling price for the plywood=$500

We know that selling price=cost price ÷(1-margin)

Let the cost price be x

[tex]x=500(1-\frac{37.5}{100} )\\x=312.50[/tex]

The cost price is $ 312.50 .

Now cost of fence = $10

Selling price of fence=cost price÷(1-margin)

substituting the values we get:

Selling price =10÷0.625

or, selling price= $16

Therefore the selling price is $16 .

Now we know that Markup percentage= profit÷ cost price

Substituting the values we get:

[tex]60\% = \frac{50}{CP}\\or,\frac{60}{10}=\frac{50}{CP}\\or,CP=83.33[/tex]

Therefore sell price=cost price+ profit

or, sell price=83.33+50

or, sell price =133.33

The sell price is $133.33

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Answer: 85 in

Step-by-step explanation:

A=Area of rectangle. L=length of rectangle. W=width of rectangle

A=L*W

1445=L*17

1445/17=L*17/17

L=85 in

Answer:

  45

Step-by-step explanation:

You want the product of 6+3i and its conjugate.

The conjugate of a complex number is created by reversing the sign of the imaginary part.

  (6 +3i)* = 6 -3i

The product of a complex number and its conjugate is recognizable as the factored form of the difference of squares:

  (6 +3i)(6 -3i) = (6)² -(3i)²

Of course, i² = -1, so this becomes ...

  6² -(3i)² = 36 -(-9) = 36 +9 = 45

The product of 6+3i and its conjugate is 45.

__

Additional comment

The product of a complex number and its conjugate is the sum of the squares of the magnitudes of the real and imaginary parts. It is always a real number. This fact is used to simplify expressions involving complex numbers.

Answer:6.986

Step-by-step explanation:

To find the standard deviation of a set of data I find it easiest to make a chart. First you must find the mean of your data. In this case it is 476.85. Then you must subtract the mean from each data point, and square each number. Now you take your new set of data that has been squared and find the mean of these numbers. This is 48.8006. Lastly, take the square root of this number. In this case your standard deviation is 6.986.

Answer: Standard deviation is 6.986.

Step-by-step explanation:

Given an data 69.2,85.2,85.2,73.8,57.9,42.6,59,67.2,85.2,61 and have to calculate standard deviation

To find the standard deviation of a set of data I find it easiest to make a chart. First you must find the mean of your data. In this case it is 476.85. Then you must subtract the mean from each data point, and square each number.

Now you take your new set of data that has been squared and find the mean of these numbers. This is 48.8006. Lastly, take the square root of this number.

In this case standard deviation is 6.986.

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Answer: Raise

5

to the power of

4

= 625

Answer:

[tex]5^{4} =625..[/tex]

Step-by-step explanation:

[tex]5^{4} = 625[/tex]

[tex]=625[/tex]

hopefully this helps you :)

Answer:

Step-by-step explanation:

What is an angle that is adjacent to BEC?

two angles that have the same vertex and a side in common

so

angle BEA

The compound inequalities for all the balls that are sports regulated are  { (x,y) : 2(1/2) ≤ x ≤ 2(5/8) and 2 ≤y≤ 2(1/6) } for Tennis ball.

{ (x,y) : 2(7/8) ≤ x≤ 3 and 5≤ y ≤ 5(1/4) } for Baseball.

{ (x,y) : 9.07 ≤ x ≤ 9.23 and 20 ≤ y ≤ 22 } for women's Basket ball.

{ (x,y) : 21.64 ≤x ≤ 22.28 and 14.46 ≤ y ≤ 15.87 } for Scoccer Ball.

Suppose we are given { (x,y) : 9.07 ≤ x ≤ 9.23 and 20 ≤ y ≤ 22 } this reads as The set of all x comma y such that x is between this range and y is between in this range.

Sports regulations have some rules that the diameters and weights of sports pieces of equipment must lie between the regulations that have been set.

We are denoting the Diameters of the balls as x in inches and the weights of the balls as y in ounces.

Now for a Tennis ball the range for x and y can be written in roaster form of set is { (x,y) : 2(1/2) ≤ x ≤ 2(5/8) and 2 ≤y≤ 2(1/6) }.

For Baseball it is { (x,y) : 2(7/8) ≤ x≤ 3 and 5≤ y ≤ 5(1/4) }.

For women's Basketball it is { (x,y) : 9.07 ≤ x ≤ 9.23 and 20 ≤ y ≤ 22 }.

For Soccer ball the set in roaster form can be written as

{ (x,y) : 21.64 ≤x ≤ 22.28 and 14.46 ≤ y ≤ 15.87 }.

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Answer:

c. Fence posts with a cost of $10 would sell for how much?

Step-by-step explanation:

Answer:3

Step-by-step explanation:easy 2 cups of pj plus cranberry juice is 3, get 6 by adding 3 again

At this point, the canoe will be under a net force of 51.52 N.

The total mass of a canoe and a paddler is 100.0 kg. A river that runs from east to west is where the canoe is thrown in. The power of the water current on the canoe is 18.0 N. The paddler exerts a force of 36.0 N [E 37.0° N].

The Free Body Diagram is then displayed below.

The canoe's net force would then be indicated as follows:

F = (18 + 36 cos 37°) i + (36 sin 37°) j

F = 46.75 i + 21.67 j

Therefore the force's strength will be

|F| = √(46.75² + 21.67²)

|F| = √2655.15

|F| = 51.52 N

Thus, at this point, the canoe will be under a net force of 51.52 N.

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Answer:

The answer is $21,854. 35

Step-by-step explanation:

rate = 14.2%

Time = 3 years

Value = 34600

V = (1-r)^t

V=34600(1-0.142)^3

V=34600 (0.858)^3

V=$21,854.35

The Isosceles triangle length of a² will be equal to (32 - 16√2).

What is an isosceles triangle?

The triangle in which the two opposite sides are equal and the two opposite angles are equal is called the isosceles triangle.

A triangle that has at least two sides of equal length is said to be isosceles. Sometimes it is stated to have exactly two sides that are the same length, while other times it is stated to have at least two sides that are the same length, with the latter version mentioning the equilateral triangle as an exception.

It is given that in an isosceles triangle abc has a=π/4 and b=c=4. Then the value of a² will be calculated as below:-

Using the cosine formula to calculate the value of a².

a² = b² + c² -2bc cosФ

a² = 16 + 16 - 2(4)(4)cos(π/4)

a² = 32 - ( 32 x {√2/2})

a² = 32 - 16√2

Therefore, the length of a² will be equal to (32 - 16√2).

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Answer:

4^2(2-root2)

Step-by-step explanation:

The percent of juniors whose score is at least 71 % is 69.15 %.

We are given that:

Test of the students are normally distributed.

Mean = μ = 71

Standard deviation = σ = 5

We need to find the percent of juniors whose score is at least 71 %.

Now, we know that:

z = ( x - μ) / σ

z = 100 - 71 / 5

z = 29 / 5

z = 5.8

So, percentage = 69.15 %

Therefore, we get that, the percent of juniors whose score is at least 71 % is 69.15 %.

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Answer: 30%

Step-by-step explanation: just add the 20% and 10% and you get 30%

Using their concepts, we have that the measures are given as follows:

a) Mean of 1.0126.

b) Average deviation of 0.01632.

c) Percent deviation of 1.6%.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

For this problem, the 5 observations are given as follows:

1.040, 0.989, 1.009, 1.026, 0.999.

Hence the mean is given by:

M = (1.040 + 0.989 + 1.009 + 1.026 + 0.999)/5 = 1.0126.

The average deviation of a data-set is given by the sum of the absolute values of the difference between each value and the mean, divided by the number of observations.

Hence:

Ad = (|1.040-1.0126| + |0.989-1.0126| + |1.009-1.0126| + |1.026-1.0126| + |0.999-1.0126|)/5 = 0.01632.

The percent deviation of a data-set is given by the absolute deviation divided by the mean and multiplied by 100%.

Hence:

0.01632/1.0126 x 100% = 1.6%.

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Answer:

7)B

8)B

9)A

10)C

Step-by-step explanation:

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